Theorems · Theorem · order theory
iInf_emptyset
∀ {α : Type u_1} {β : Type u_2} [inst : CompleteLattice α] {f : β → α}, ⨅ x ∈ ∅, f x = ⊤- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Top.topstatement and proof · cited by 9,680
- iInfstatement and proof · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- iInf_congr_Propproof · cited by 218
- Set.mem_empty_iff_falseproof · cited by 32
- iInf_negproof · cited by 27
- iInf_topproof · cited by 21
Cited by3
Results whose statement or proof uses this declaration.
- Metric.infEDist_emptyproof · cited by 6
- Set.biInter_emptyproof · cited by 1
- Filter.countable_biInf_eq_iInf_seq'proof · cited by 1